Consider a simple economy with search unemployment. The matching function is given by M = 0.1Q 4/12A 8/12 The supply curve of the workers is given by v(Q) = Q 2/6 Let b = 0.4, z = 1, k = 0.05, e= 0.1 and a = 0.5, where k is the cost of creating a vacancy.

1. Calculate the market tightness j. Show your calculation in detail.[10 points]

2. what is the job-finding probability?[10 points]

3. what is the vacancy rate?[5 points]

4. what is the expected payoff for the worker?[5 points]

5. Suppose there is a technological change that increases the productivity z. Using the DMP model, determine the effects on the unemployment rate, the vacancy rate, the labour force, the number of firms, and labour market tightness. Use diagrams, and explain your results.[10 points] 6. Suppose there is a decrease in matching efficiency. Using the DMP model, determine the effects on the unemployment rate, the vacancy rate, the labour force, the number of firms, and labour market tightness. Use diagrams, and explain your results.[10 points]

Problem 1: Search and unemployment (50 points) Consider a simple economy with search unemployment. The matching function is given by M = 0.104/12 48/12 The supply curve of the workers is given by "(Q) = Q2/6 Let b = 0.4, z = 1, k = 0.05, e= 0.1 and a = 0.5, where k is the cost of creating a vacancy. 1. Calculate the market tightness j. Show your calculation in detail. [10 points] 2. what is the job-finding probability? [10 points] 3. what is the vacancy rate?[5 points] 4. what is the expected payoff for the worker? [5 points] 5. Suppose there is a technological change that increases the productivity z. Using the DMP model, determine the effects on the unemployment rate, the vacancy rate, the labour force, the number of firms, and labour market tightness. Use diagrams, and explain your results. [10 points] 6. Suppose there is a decrease in matching efficiency. Using the DMP model, determine the effects on the unemployment rate, the vacancy rate, the labour force, the number of firms, and labour market tightness. Use diagrams, and explain your results. [10 points]